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In triangle ABC, point X is the midpoint of side AC and [#permalink]
01 Aug 2008, 03:27

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In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangle region RCS(1) the area of triangular region ABX is 32(2) the length of one of the altitudes of triangle ABC is 8A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.D. Each Statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.

In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangle region RCS(1) the area of triangular region ABX is 32(2) the length of one of the altitudes of triangle ABC is 8A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.D. Each Statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.

IMO A given that RCS is similar to YXC ,YXC is similar to BCX which is similar to ABC.(1) gives area of ABX which can be used to get area of RCS since these are all similar triangles(2) does not indicate are but just the altitude hence cant help in finding are of RCS

IMO A . Reason : as ACB and RCS are symitrical triangles, there sides will be proportionate ( ratio 1:4 ).. and so area will be also propotionate , but with a square.. i.e 1: 16.. as the area of ACB is 64 as per statement 1, the area of RCS it bill be 4. statement 2 is not sufficient as the altitue can be any of the 3.

In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangle region RCS(1) the area of triangular region ABX is 32(2) the length of one of the altitudes of triangle ABC is 8A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.D. Each Statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.

IMO A given that RCS is similar to YXC ,YXC is similar to BCX which is similar to ABC.(1) gives area of ABX which can be used to get area of RCS since these are all similar triangles(2) does not indicate are but just the altitude hence cant help in finding are of RCS

In an earlier reply :given that RCS is similar to YXC ,YXC is similar to BCX which is similar to ABC.(1) gives area of ABX which can be used to get area of RCS since these are all similar triangles(2) does not indicate are but just the altitude hence cant help in finding are of RCS